KIEV, Ukraine - Ukraine's president said Sunday that intercepted radio and telephone conversations prove that Russia-backed separatists were responsible for firing the rockets that pounded the southeastern city of Mariupol and killed at least 30 people.

The attack on Mariupol, a strategically situated port city that had been relatively quiet for months, alarmed the West and looked likely further to aggravate relations with Russia.

Putting the blame squarely on Moscow, President Barack Obama said the U.S. would work with its European partners to "ratchet up the pressure on Russia."

European Union foreign affairs chief Federica Mogherini later announced that EU foreign ministers would hold an "extraordinary" meeting in Brussels on Thursday to discuss Ukraine.

Russian Foreign Minister Sergei Lavrov, speaking separately with Mogherini and U.S. Secretary of State John Kerry, told them the Ukrainian government bore responsibility for the latest military escalation, according to statements released by his ministry. Lavrov did not, however, directly address who had carried out the attack on Mariupol and said that it should be investigated.

Separatist leader Alexander Zakharchenko initially announced that his forces had begun an offensive on the government-controlled city of Mariupol. But after the extent of civilian casualties became known, he backtracked and blamed Ukrainian forces for Saturday's carnage.

The rocket attack came a day after the rebels rejected a peace deal and announced they were going on a multi-pronged offensive against the Kiev government in Kiev in a bid to seize more territory. The rebel stance has upended European attempts to mediate an end to the fighting in eastern Ukraine that has cost at least 5,100 lives since April, according to United Nations estimates.

"The intercepted radio and telephone conversations, which were given to me by Ukraine's security services, irrefutably prove that the attack was conducted by the terrorists, who, unfortunately, are supported by Russia," President Petro Poroshenko said during an emergency meeting of his Security Council.

The Organization for Security and Cooperation's monitoring mission said Saturday that the Grad and Uragan rockets that hit Mariupol were fired from areas under rebel control. The OSCE said its Permanent Council would meet Monday in Vienna "in light of the rapid deterioration of the situation in eastern Ukraine."

In Mariupol on Sunday, emergency workers disposed of rocket fragments left by the attack. Police said two unexploded rockets were found in a bank and an apartment building.

U.N. refugee agency workers handed out blankets to people left homeless or without heat because of the shelling, which hit schools, homes and shops.

"The city is in shock," Mariupol resident Yelena Khorshenko said by telephone. "The streets are empty, and people are boarding up their windows and preparing for the worst."

Mariupol lies between Russia and the Russian-annexed Crimean Peninsula. Heavy fighting in the region in the fall raised fears that the Russian-backed separatists would try to capture the city to forge a land link between the two.

In Kiev, hundreds gathered on the central square in memory of those who died in Mariupol. In addition to the 30 people killed, 95 people were wounded.

A peace deal signed in September in Minsk, Belarus, envisaged a cease-fire and a pullout of heavy weapons from a division line in eastern Ukraine, but both sides have repeatedly violated the pact.

The U.S. is "deeply concerned about the latest break in the cease-fire and the aggression that these separatists with Russian backing, Russian equipment, Russian financing, Russian training and Russian troops are conducting," Obama said during a visit to New Delhi.

"And we will continue to take the approach that we've taken in the past, which is to ratchet up the pressure on Russia and I will look at all additional options that are available to us short of military confrontation and try to address this issue."

Obama said the U.S. would work "in close consultation with our international partners, and particularly European partners, to ensure that they stay in lock-step with us on this issue."

The U.S. and EU have imposed sanctions on Russian individuals, businesses and entire sectors of the economy over Russia's annexation of Crimea and role in fomenting the conflict in eastern Ukraine.

Lavrov, in the separate calls with Kerry and Mogherini, attributed the latest violence to stepped-up operations by the Ukrainian military. He urged the West to pressure Ukraine to engage in comprehensive talks for a political solution to the conflict, the ministry statements said.

Kerry told Lavrov that the U.S. was ready to participate in serious efforts to settle the conflict, but made clear that "Russia will be judged by its actions and that the costs to Russia will only increase of attacks continue," the State Department said.

In another indication of Western alarm over the latest violence, German Chancellor Angela Merkel called both Poroshenko and Russian President Vladimir Putin on Sunday. Merkel expressed her condolences to Poroshenko for the latest civilian deaths, her spokesman Steffan Seibert said.

"During her call with President Putin the chancellor urged him to avoid a further escalation and to exert influence on the separatists in order to achieve the implementation of the Minsk agreement," the spokesman said.

Fighting also has intensified for control over Debaltseve, a government-held town and railway hub about 50 kilometers (30 miles) east of Donetsk, the main city under separatist control.

Ukraine military spokesman Andriy Lysenko said rebel shelling had killed an undetermined number of civilians and damaged 60 residential buildings. He said there was no electricity or heat in the city of 25,000 people.

Four Ukrainian servicemen were killed and 17 wounded over the past 24 hours, Lysenko said.